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Graph rigidity and distributed formation stabilization of multi-vehicle systems

Olfati-Saber, Reza and Murray, Richard M. (2002) Graph rigidity and distributed formation stabilization of multi-vehicle systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, December 10-13, 2002, Las Vegas, Nevada, USA. Vol.3. IEEE , Los Alamitos, CA, pp. 2965-2971. ISBN 0-7803-7516-5.

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We provide a graph theoretical framework that allows us to formally define formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formation and an appropriate potential function associated with the formation. This allows formulation of meaningful optimization or nonlinear control problems for formation stabilization/tacking, in addition to formal representation of split, rejoin, and reconfiguration maneuvers for multi-vehicle formations. We introduce an algebra that consists of performing some basic operations on graphs which allow creation of larger rigid-by-construction graphs by combining smaller rigid subgraphs. This is particularly useful in performing and representing rejoin/split maneuvers of multiple formations in a distributed fashion.

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Murray, Richard M.0000-0002-5785-7481
Additional Information:© Copyright 2002 IEEE. Reprinted with permission. Posted online: 2003-03-10
Subject Keywords:algebra; distributed formation stabilization; graph realizations; graph rigidity; graph theory; multivehicle systems; nonlinear control problems; reconfiguration maneuvers; rejoin maneuvers; shape variables; split maneuvers
Record Number:CaltechAUTHORS:OLFcdc02b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5151
Deposited By: Archive Administrator
Deposited On:03 Oct 2006
Last Modified:02 Oct 2019 23:19

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